A pseudo-elastic model for the Mullins effect in filled rubber

When a rubber test piece is loaded in simple tension from its virgin state, unloaded and then reloaded, the stress required on reloading is less than that on the initial loading for stretches up to the maximum stretch achieve d on the initial loading. This stress softening phenomenon is referred to a s the Mullins effect. In this paper a simple phenomenological model is prop osed to account for the Mullins effect observed in filled rubber elastomers . The model is based on the theory of incompressible isotropic elasticity a mended by the incorporation of a single continuous parameter, interpreted a s a damage parameter. This parameter controls the material properties in th e sense that it enables the material response to be governed by a strain-en ergy function on unloading and subsequent submaximal loading different from that on the primary (initial) loading path from the virgin state. For this reason the model is referred to as pseudo-elastic and a primary loading-un loading cycle involves energy dissipation. The dissipation is measured by a damage function which depends only on the damage parameter and on the poin t of the primary loading path from which unloading begins. A specific form of this function with two adjustable material constants, coupled with stand ard forms of the (incompressible, isotropic) strain-energy function, is use d to illustrate the qualitative features of the Mullins effect in both simp le tension and pure shear. For simple tension the model is then specialized further in order to fit Mullins effect data. It is emphasized that the mod el developed here is applicable to multiaxial states of stress and strain, not just the specific uniaxial tests highlighted.